On the blow-up for critical semilinear wave equations with damping in the scattering case

Abstract

We consider the Cauchy problem for semilinear wave equations with variable coefficients and time-dependent scattering damping in ${\mathbf{R}}^n$, where $n\ge 2$. It is expected that the critical exponent will be Strauss' number $p_0(n)$, which is also the one for semilinear wave equations without damping terms. Lai and Takamura (2018) have obtained the blow-up part, together with the upper bound of lifespan, in the sub-critical case $p<p_0(n)$. In this paper, we extend their results to the critical case $p=p_0(n)$. The proof is based on Wakasa and Yordanov (2018), which concerns the blow-up and upper bound of lifespan for critical semilinear wave equations with variable coefficients.

9 pages

References in corpus (5)

• Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent
• A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent
• Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case
• Blow-up of solutions to critical semilinear wave equations with variable coefficients
• Global existence for semilinear damped wave equations in relation with the Strauss conjecture

Cited by in corpus (3)

• Blow-up for a weakly coupled system of semilinear damped wave equations in the scattering case with power nonlinearities
• Lifespan of semilinear generalized Tricomi equation with Strauss type exponent
• Global existence for semilinear damped wave equations in relation with the Strauss conjecture